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While there are many different ways to approach this question, I think the best approach is from a very high-level as it gives you the proper foundation upon which you can build your exercise routine.

An easy way you can understand how muscles are built is by applying Selye's Theory of the General Adaptive Syndrome. The process can be broken down into three stages:

General Adaptive Syndrome

Stage One (Alarm): this is where you shock your muscles through stress (exercise). If the weight is insufficient, then the body will not become shocked and it will not enter stage two. In contrast, if the weight is too excessive, it will overload the body and you will find yourself headed to Stage 3 (exhaustion).

Stage Two (Resistance): this is where your body responds to the stressor in stage one through various hormonal and metabolic activity, and on a basic level is preparing your body for future exposure to that stress.

Stage Three (Exhaustion): if the stress on your body is too great or too frequent, then your body will not be able to recover from the stress and exhaustion sets in. With respect to magnitude, it is when you lift weights too heavy for your current muscles; with respect to frequency, it is when you do not properly recover before your next workout (see road to recovery below). This stage is commonly referred to as overtraining and must be avoided.

Stage Three (Recovery): if you use appropriate weights to trigger the stress and have adequate rest before your next workout, then you go into the recovery stage where the muscles are made. With new and improved muscles, you are now more prepared for future stress.

Drawing Conclusions

From this we can see that too little weight produces no effect, whereas too much weight or poor recovery results in overtraining, therefore the best approach to build muscle is using the proper amount of weight and appropriate recovery following the workout.

Furthermore, we can deduce that as your body recovers and builds muscle, you will require progressively heavier weights in order to trigger stress and continue to build muscle.

It is important to realize that in these stages, muscle is not made during the workout (Alarm), it is made in the time afterwards while you are recovering from the stress. Therefore, even the best structured workout plan can fall short if the trainee does not take the necessary steps to recover!

Road to recovery

The road to recovery is paved with several stones: sleep (8-9 hours/day), rest days between workouts (1-2 days for the novice, scaling higher for intermediate/advanced), and a proper diet (lots of protein [1-2g per kg of bodyweight], 500-1000 caloric excess to fuel muscle growth, micronutrients, and stay well hydrated).

Summary

For someone just starting out (novice) you will be able to adapt very quickly to stress, and thus only need 1 or 2 days rest between workouts. Also, you will see your greatest strength/muscle gains during this time. Depending on your ultimate goals (muscle mass, strength, power) there are loads of different and proven exercise routines to choose from that will provide you a progressively scaling workout to follow. I've had personal success with StrongLifts and Starting Strength, which are full body barbell routines designed for strength and come highly recommended on this site, but your goals or mileage may vary.